Thread: Mapping vector spaces

Hi!

I have a problem with this math task:

Linear transformation maps basic vectors to vectors (2,−3,−5), (0, 4, 8) and (2, 9, 2).
In which vector (vx, vy, vz) does vector (-3, 9, -1) maps?


(sorry for my BAD English)

Originally Posted by T-Mac

Hi!

I have a problem with this math task:

Linear transformation maps basic vectors to vectors (2,−3,−5), (0, 4, 8) and (2, 9, 2).
In which vector (vx, vy, vz) does vector (-3, 9, -1) maps?


(sorry for my BAD English)

I do not understand the problem.

Originally Posted by T-Mac

Hi!

I have a problem with this math task:

Linear transformation maps basic vectors to vectors (2,−3,−5), (0, 4, 8) and (2, 9, 2).
In which vector (vx, vy, vz) does vector (-3, 9, -1) maps?


(sorry for my BAD English)

You are looking for a linear transformation L that takes
L(2, -3, -5) = (0, 4, 8)
L(0, 4, 8) = (2, 9, 2)

and looking for the vector v = (vx, vy, vz) such that
L(vx, vy, vz) = (-3, 9, -1)

Is this correct?

-Dan

topsquark, yes.

Originally Posted by T-Mac

Hi!

I have a problem with this math task:

Linear transformation maps basic vectors to vectors (2,−3,−5), (0, 4, 8) and (2, 9, 2).
In which vector (vx, vy, vz) does vector (-3, 9, -1) maps?


(sorry for my BAD English)

now i'm a little rusty on linear algebra, so correct me if i'm wrong. you said topsqaurk was right, so we are given that:
L(2, -3, -5) = (0, 4, 8)
L(0, 4, 8) = (2, 9, 2)

however, the standard matrix for L will be a 3x3 matrix, and therefore, we need at least 3 examples of transformations to find it.

unless there was some other way which i am not remembering at the moment